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For while their basic idea of describing behavior in terms of mathematical equations works well in cases like planetary motion where the behavior is fairly simple, it almost inevitably fails whenever the behavior is more complex.
Presumably most of the processes that are important take place while leaves are still folded up inside buds, and are not yet very solid.
This basic mechanism may well be the main one at work in many biological systems: each cell or each organism becomes separated from others, and while it survives, it can exhibit organized behavior.
So while in a system like a cellular automaton one typically imagines that a new and separate state of the system is somehow produced at each step in time, present-day physics more tends to think of the complete history of the universe throughout time as being just a single structure laid out in the four dimensions of spacetime.
But while this view is closer to our everyday perception of time, it seems to
And while at some level the structure can be spread out in the network, the point is that it must always in effect have a localized core with the form shown in the second picture.
And while one expects that sufficiently large networks should in some sense act on average like continuous space, it is far from clear at first how the kinds of properties of relevance to general relativity will emerge.
But while the mathematical structure of general relativity is complicated enough that it is often difficult to see just where in spacetime effects come from, it is usually assumed that matter is somehow ultimately required to provide a source for gravity.
And while persistent structures can be thought of as corresponding to real particles, intermediate structures are in many ways like the virtual particles of traditional particle physics.
In particular, it might be thought that the behavior of systems like rule 30—while obviously at least somewhat computationally sophisticated—might somehow be too random to be harnessed to allow complete universality.